Problem 1. Maximum-likelihood methods apply to estimates of prior probabilities as well. Let samples be drawn by successive, independent selections of a state of mature w; with unknown probability P(w;), i = 1, 2, ... , M. Let zak = 1 if the state of nature for the kth sample is w; and zix = 0 otherwise. (a) Show that 72 P(21, ..., zin P(w )) = [[ P(w.)=* (1 - P(w;)) -zik. k=1 (b) Show that the maximum-likelihood estimate for P(w;) is P(wi) = Zik. K= 1 Interpret your result in words